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Hankel operators and the Dixmier trace on the Hardy space

M. Englis ; Genkai Zhang (Institutionen för matematiska vetenskaper, Analys och sannolikhetsteori)
Journal of the London Mathematical Society (0024-6107). Vol. 94 (2016), p. 337-356.
[Artikel, refereegranskad vetenskaplig]

We give criteria for the membership of Hankel operators on the Hardy space on the disc in the Dixmier class, and establish estimates for their Dixmier trace. In contrast to the situation in the Bergman space setting, it turns out that there exist Dixmier-class Hankel operators that are not measurable (that is, their Dixmier trace depends on the choice of the underlying Banach limit), as well as Dixmier-class Hankel operators that do not belong to the Schatten-Lorentz ideal. A related question concerning logarithmic interpolation of Besov spaces is also discussed.

Denna post skapades 2016-12-05.
CPL Pubid: 245828


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